A probabilistic interpretation of a sequence related to Narayana polynomials

2012/02/06 by Tewodros Amdeberhan, T. Amdeberhan, Amdeberhan, T. +6
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1202.1203

openalex publication_date 2012/02/06 · arxiv created 2012/03/20 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A sequence of coefficients appearing in a recurrence for the Narayana polynomials is generalized. The coefficients are given a probabilistic interpretation in terms of beta distributed random variables. The recurrence established by M. Lasalle is then obtained from a classical convolution identity. Some arithmetical properties of the generalized coefficients are also established.

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